Question

explain
challenge problem
drinks at bens beans have a mean sugar content of 20 g with a standard deviation of 6 g. the sugar content in a grande cappuccino at bens beans has a z-score of $-0.75$ compared to the rest of the drinks at that shop.
how much sugar is in a grande cappuccino at bens beans?
____ grams
check

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $z$ is the z-score, $x$ is the value we want to find, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Plug in known values

We know $z=-0.75$, $\mu=20$, $\sigma=6$. Substitute these into the formula:
$-0.75 = \frac{x - 20}{6}$

Step3: Solve for $x$

Multiply both sides by 6:
$-0.75 \times 6 = x - 20$
$-4.5 = x - 20$
Add 20 to both sides:
$x = 20 - 4.5$

Answer:

15.5 grams